Introduction Scientific Computing (WISB356), 2025/2026

Location and time

Monday 13:15-17:00 and Thursday 9:00-12:45 starting on Monday April 20, 2026. Please check MyTimeTable for the scheduled locations at the Uithof!

Teachers

Module 1: Paul Zegeling
Module 2: Alexandra Holzinger
Teaching assistant: Aurora Faure Ragani

Course material and software

In both modules we use Matlab, see Free software at the UU for students. Please install Matlab before the lectures start! And bring your own laptop!

Information

All information on module 1 can be found on the present page. Information on module 2 can be found on Alexandra Holzinger's ISC webpage (more info for this part of the course: to be added by end of April 2026).

Grading

Based on two reports, one per module. Report 1 and Report 2 have equal weight and count for 50% of the final grade of the course. Each of the reports needs to obtain a grade of at least 5, and the rounded final grade must be at least 6. The reports can be written in either Dutch or English.

Credits

7,5 ECTS

Description

The aim of this course is to provide a first orientation towards the area of scientific computing by some case studies from various application areas. Topics treated are widely used techniques from numerical linear algebra such as the solution of linear systems and eigenvalue problems, within the context of an application such as computing the square root of a matrix (connected to fractional derivatives and Levy flights in epidemiology simulation models). We will also study algorithms for numerically solving space-fractional (and other) partial differential equations. Both theoretical aspects and practical, software-related aspects will be treated. Every week there will be frontal lectures alternating with exercise/computer laboratory classes. This course presents a taste of the master track Applied Mathematics, Complex systems, and Scientific Computing and it represents an overview of scientific computing.

Prerequisites

Calculus and Linear algebra 1 and 2 (WISB107 and WISB108) and Programmeren in de Wiskunde (WISB152).
In addition, the Bachelor courses Numerieke Wiskunde (WISB251) and Probability Theory (WISB161) could be very useful.
It is not necessary to know Matlab already, as we will start with a gentle introduction to Matlab. Warning: be aware that the level of difficulty of the course will gradually increase during the period of the course, both conceptually and practically, so that near the end (in the second module) we expect the maximum effort from the student.

Schedule

We roughly follow the schedule below. Ch5 means Chapter 5 from the book by Cleve Moler, "Experiments with Matlab", 2011. Small changes may still occur depending on our progress.

Module 1

We begin with an introduction in Matlab: Chapters 1, 2 (basic calculations, functions, plotting) and Chapters 4, 5 (matrices, linear systems) from the online book by Cleve Moler (2011), Experiments with Matlab. Next, we continue with nonlinear solvers for scalar equations, systems and matrix equations. These will be applied to solve space-fractional partial differential equation models from practice.

Day 1 (Monday April 20, 2026):
Introduction to Matlab (Ch1 and Ch2)

Iterations, logistic equation, chaotic behaviour, Fibonacci sequence, plotting, while/if, flow diagrams.
Demos from .m files from the book.
Today's lecture notes (will be added Monday April 20).
Some additional notes on Matlab (in Dutch).
Exercise 1a on the use of the "abc-formula" for solving quadratic equations. 1a (English version).
Exercise 1b to "simulate" a hurricane. 1b (English version).
Exercise 1c on the logistic differential equation (DE). An explanation of the different options to treat the logistic DE numerically.
Create a matlab file to solve this problem (make graphs of the solution values as a function of the index).
An interesting video on the logistic differential equation that explains the (possible) chaotic behaviour and its applications in many areas.
Extra (optional) exercises to practice basic Matlab commands: exercises Ch1: 1, 6, 9, 10, 15 and Ch2: 3, 4, 5, 6, 7, 8.
Useful slides: A quick introduction to Matlab, Johns Hopkins University, Computer Science Dept. 2007

Day 2 (Thursday April 23, 2026)
Matrix laboratory and linear systems (Ch4)

Matrices and Matlab
Solving systems, finding eigenvalues, determinants, norms, etc
Euler Backward, Method of Jacobi
Exercise 2a on a basic method for solving linear systems (Jacobi method). More information can be found here.
Be sure to finish first exercises 1a, 1b, 1c from Day 1, before starting to work on the following:
extra (optional) exercises Ch4: 2, 3, 4, 5, 8, 14.
Useful videos on linear algebra: Essence of linear algebra by 3Blue1Brown, a YouTube channel on animating mathematics.
Additional useful slides: Solving Systems of Linear Equations by Greg Fasshauer, Illinois Institute of Technology.

Monday April 27:
no lecture today! ("Koningsdag")

Day 3 (Thursday April 30, 2026):
Nonlinear equations

Basic methods and their properties
Continuous Newton versus Euler-Forward
Two dimensions, the complex version and Newton fractals

Day 4 (Monday May 4, 2026):
Reaction-diffusion equations

Finite-difference matrices and the Method-of-Lines: the matrices D1 and D2
Numerical stability: Euler-Forward vs Euler-Backward
IMEX method for nonlinear PDEs
Applications: Fisher PDE from population dynamics and a non-equilibrium model from geo-hydrology

Day 5 (Thursday May 7, 2026):
Square roots of matrices

Finite-difference (FD) matrices
Square root(s) of some matrices
Matrix-Newton method (stable or unstable?)
Denman-Beavers algorithm

Day 6 (Monday May 11, 2026):
Space-fractional heat and blow-up equations

Fractional derivatives, the fractional Laplacian, applications
The finite-difference matrix D3
The Matlab functions expm and sqrtm; square roots of FD-matrices
Gelfand-Bratu model, bifurcation diagrams
Sundman transformation

Thursday May 14:
no lecture today! ("Hemelvaartsdag")

Day 7 (Monday May 18, 2026; between 13:15 and 15:00): Questions can be asked about Project 1 (for Report 1).

You can find the information about Project 1 of Module 1 here (not yet available).

The deadline for Report 1 is FRIDAY May 22 23:59; via e-mail to P dot A dot Zegeling AT uu dot nl in ONE pdf-file! (Matlab codes in the Appendix of the report).

Last update of this page by Paul Zegeling: April 13, 2026.